SIM(2)-invariant modifications of electrodynamic theory

In the Cohen-Glashow Very Special Relativity we exhibit possible modifications to the Maxwell theory and to the quantum electrodynamics Lagrangian in some generality, and discuss characteristic features depending on the modifications. Modified gauge transformations in SIM(2)-invariant theories are introduced and the related gauge fields, with two polarization states, can have nonzero mass. Also considered are SIM(2)-covariant modifications to the Proca-type field equations for a massive spin-1 particle.